用深度学习实现高鲁棒性可逆水印，嵌入效率提升55倍。

Robust Reversible Watermarking (RRW) enables perfect recovery of cover images and watermarks in lossless channels while ensuring robust watermark extraction in lossy channels. Existing RRW methods, mostly non-deep learning-based, face complex designs, high computational costs, and poor robustness, limiting their practical use. This paper proposes Deep Robust Reversible Watermarking (DRRW), a deep learning-based RRW scheme. DRRW uses an Integer Invertible Watermark Network (iIWN) to map integer data distributions invertibly, addressing conventional RRW limitations. Unlike traditional RRW, which needs distortion-specific designs, DRRW employs an encoder-noise layer-decoder framework for adaptive robustness via end-to-end training. In inference, cover image and watermark map to an overflowed stego image and latent variables, compressed by arithmetic coding into a bitstream embedded via reversible data hiding for lossless recovery. We introduce an overflow penalty loss to reduce pixel overflow, shortening the auxiliary bitstream while enhancing robustness and stego image quality. An adaptive weight adjustment strategy avoids manual watermark loss weighting, improving training stability and performance. Experiments show DRRW outperforms state-of-the-art RRW methods, boosting robustness and cutting embedding, extraction, and recovery complexities by 55.14\(\times\), 5.95\(\times\), and 3.57\(\times\), respectively. The auxiliary bitstream shrinks by 43.86\(\times\), with reversible embedding succeeding on 16,762 PASCAL VOC 2012 images, advancing practical RRW. DRRW exceeds irreversible robust watermarking in robustness and quality while maintaining reversibility.